Results 61 to 70 of about 16,375 (207)
Homoclinic intersections and indecomposability [PDF]
Proceedings of the American Mathematical Society, 1987 The closure of a one-dimensional unstable manifold of a hyperbolic fixed point of a diffeomorphism having homoclinic points is, under mild assumptions, shown to be an indecomposable continuum. As a result, dynamical systems possessing such behavior cannot be modeled using inverse limits based on any simple space.
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International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.This study examines the second‐order Kuramoto model within a specific small invariant subspace. We explore how the damping parameter influences the emergence of synchronized states and the weak chimera state in this model. In addition, we numerically investigate various behaviors in the phase space resulting from changes in the damping parameter and ...
Mary G. Thoubaan +4 more
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Multibump solutions for an almost periodically forced singular Hamiltonian system
Electronic Journal of Differential Equations, 1995 existence of so-called multibump homoclinic solutions for a family of singular Hamiltonian systems in $R^2$ which are subjected to almost periodic forcing in time.
Paul H. Rabinowitz
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Frequency spanning homoclinic families [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2003 A family of maps or flows depending on a parameter $ $ which varies in an interval, spans a certain property if along the interval this property depends continuously on the parameter and achieves some asymptotic values along it. We consider families of periodically forced Hamiltonian systems for which the appropriately scaled frequency $\bar ( )$ is
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Variational approximations to homoclinic snaking [PDF]
Physical Review E, 2011 4 pages, 3 figures ...
Susanto, H., Matthews, P. C.
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This study presents the dynamic analysis of stochastic fractional unstable nonlinear Schrödinger equation (SFuNLSE), focusing on the analysis of bifurcation, chaotic nature, return map, recurrence plots, strange attractor, basin attractor, power spectrum, chaotic nature and also finds the exact optical soliton solution with multiplicative noise ...
Md. Mamunur Roshid +3 more
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Existence and multiplicity results for homoclinic orbits of Hamiltonian systems
Electronic Journal of Differential Equations, 1997 Homoclinic orbits play an important role in the study of qualitative behavior of dynamical systems. Such kinds of orbits have been studied since the time of Poincare.
Chao-Nien Chen, Shyuh-Yaur Tzeng
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Homoclinic Solutions for a Class of Nonlinear Difference Equations
Journal of Applied Mathematics, 2014 We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach.
Ali Mai, Zhan Zhou
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Hyperbolic periodic points for chain hyperbolic homoclinic classes
, 2015 In this paper we establish a closing property and a hyperbolic closing property for thin trapped chain hyperbolic homoclinic classes with one dimensional center in partial hyperbolicity setting.
Sun, Wenxiang, Yang, Yun
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Homoclinic snaking in bounded domains [PDF]
Physical Review E, 2009 Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once
Houghton, S.M., Knobloch, E.
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